Question 6
Let $ABC$ be an acute triangle with circumcircle $\Gamma$. Let $\ell$ be a tangent line to $\Gamma$, and let $\ell_a$, $\ell_b$, $\ell_c$ be the lines obtained by reflecting $\ell$ in the lines $BC$, $CA$, and $AB$, respectively. Show that the circumcircle of the triangle determined by the lines $\ell_a$, $\ell_b$, and $\ell_c$ is tangent to the circle $\Gamma$.